Summary
The effect of blowing/suction on steady two-dimensional laminar non-Darcy forced convection flow over a flat plate with variable wall temperature in a porous medium is numerically analyzed. The nonlinear uncoupled boundary-layer equations were transformed, and the resulting partial differential equations were solved by Keller box method. Numerical results for the dimensionless velocity profiles, the temperature profiles, the local friction coefficient and the local Nusselt number are presented for various combinations of parameters. In general, it is observed that in the suction (blowing) case both the local friction coefficient and the local Nusselt number increase (decrease). The local Nusselt number is more sensitive to the blowing/suction parametersf w than the local skin friction coefficient. The local Nusselt number enhances with the increase of Rek, Pr, and λ. Moreover, the local Nusselt number becomes nearly constant when ξ is very small (pure fluid flow) and ξ is very large (pure Darcy flow).
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Abbreviations
- A :
-
Constant defined in Eq. (4.1)
- a :
-
Constant defined in Eq. (4.1)
- C f :
-
Local friction coefficient,2v(∂u/∂y) y=0 /U 2∞
- F :
-
Empirical constant in the second-order resistance
- f :
-
Dimensionless stream function defined in Eq. (7.3)
- f w :
-
Blowing/suction parameter,\({{ - 2a} \mathord{\left/ {\vphantom {{ - 2a} {\sqrt {U_\infty v} }}} \right. \kern-\nulldelimiterspace} {\sqrt {U_\infty v} }}\)
- η:
-
Local heat transfer coefficient
- K :
-
Permeability of the porous medium
- k :
-
Thermal conductivity
- Nux :
-
Local Nusselt number,hx/k
- P :
-
Pressure
- Pr:
-
Prandtl number,v/α
- q :
-
Heat flux
- Rek :
-
Modified local Reynolds number,\(U_\infty \sqrt K /v\)
- Rex :
-
Local Reynolds number,U ∞ x/v
- T :
-
Temperature
- u :
-
Velocity component in the x-direction
- U ∞ :
-
Free-stream velocity
- v :
-
Velocity component in the y-direction
- v w :
-
Surface mass flux,ax −1/2
- x :
-
Coordinate along the plate
- y :
-
Coordinate normal to the plate
- α:
-
Thermal diffusivity
- η:
-
Pseudo-similarity variable defined in Eq. (7.2)
- θ:
-
Dimensionless temperature difined in Eq. (7.4)
- λ:
-
Exponent of wall temperature
- v :
-
Kinematic viscosity
- ξ:
-
Streamwise coordinate defined in Eq. (7.1)
- ρ:
-
Density
- ψ:
-
Stream function
- w :
-
Surface condition
- ∞:
-
Condition far away from the surface
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Yih, K.A. Blowing/suction effect on non-Darcy forced convection flow about a flat plate with variable wall temperature in porous media. Acta Mechanica 131, 255–265 (1998). https://doi.org/10.1007/BF01177229
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DOI: https://doi.org/10.1007/BF01177229